Integers without divisors from a fixed arithmetic progression

2006/04/03 by William D. Banks, Banks, William D., John B. Friedlander +3
Mathematics · #11A05 #11A25 #11N37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A05 #msc:11A25 #msc:11N37

paper · pdf · doi:10.48550/arxiv.math/0604036

37 pages

arxiv created 2006/04/03 · arxiv updated 2009/12/01

Abstract

Let a be an integer and q a prime number. In this paper, we find an asymptotic formula for the number of positive integers n < x with the property that no divisor d > 1 of n lies in the arithmetic progression a modulo q.

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